ROOT FUNCTIONS Graphing And Analysis (Page 1 of 5)

Let's graph the square root function f(x) = sqrt(x^2-25). Enter this function as Y1, then try a standard window.

A comprehensive graph of a root function should show all intercepts and any terminal points. For this function, the standard window provides a good viewing rectangle. However, notice the small gaps near where the graph should intersect the x-axis at x = -5 and x = 5. These gaps are artificial. To prevent them we must create a "friendly window", one in which Xmax-Xmin is a multiple of 9.4. In this example, we can use a multiple of 2.0, meaning the width of the screen will be 2(9.4) = 18.8 units and each pixel will represent 0.2 unit. The terminal points at x = -5 and x = 5 will then be positioned directly on pixel centers. Let Xmin = -9.4 and Xmax = 9.4 (half of 18.8 is 9.4).

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